How to clean the upholstery on my 1999 Barcalounger?

I purchased at an estate sale a 1999 super sagless barcalounger which is in terrific condition. The soft leather is not worn, but is dirty especially on the arms and the hight back and head resting area. We've tried a leather cleaner which helped minimally. We have not put soap and water on it except in nonvisible area to test it, but it did not help either. Other than having these dark dirty areas, the upholstery is in excellent condition. How can we get these dark dirty areas out. My spouse says it is skin and dried sweat. Is there a self solution or an expert that can get the dirt out?